1. Workshop on the Elements of Predictability LOGISTICS BACKGROUND AND INTRODUCTION Roger Ghanem John Red-Horse Steve Wojtkiewicz Thanks to: Department of Civil Engineering at Hopkins National Science Foundation

2. Today: Lunch provided in this room Sign-up for two of tomorrow’s breakout sessions morning / afternoon Banquet in Shriver Hall: 5pm-7:30pm Restrooms Logistics Tomorrow: Lunch and coffee breaks provided in Shriver Hall Meeting rooms in Mattin Hall (three sessions) and Shriver Hall Program has been moved ahead by 30 minutes

4. Background and Introduction This is the Second Hopkins Workshop in Uncertainty-Related Research 1999 Workshop on Uncertainty Analysis and Management identified, qualitatively, components of an emerging field 2003 Elements of Predictability aim for a more quantitative and specific delineation of these components Both meetings recognize and capitalize on the multidisciplinary interests, contributions, and intrinsic nature of the relevant questions.

5. WHAT LEVEL OF ACCURACY IS CONSISTENT WITH AVAILABLE RESOURCES: DATA ANALYSIS COMPUTING WHAT LEVEL OF RESOURCES: DATA ANALYSIS COMPUTING IS REQUIRED TO ACHIEVE TARGET ACCURACY / CONFIDENCE Two sides to the problem: uncertainty quantification and management

6. PHYSICAL REALITY: SURROGATE TO REALITY: ASSUMED PHYSICS EXPERIMENTAL DATA PREDICTIVE MODEL ASSIMILATE Approximation to surrogate DecisionOBJECTIVE REPRESENT TRUNCATED INFORMATION: PROBABILISTIC MODELS, SUBSCALE, MULTISCALE MODELS.

7. TYPICAL QUESTION ENABLED BY UNCERTAINTY QUANTIFICATION AND MANAGEMENT AT WHAT LEVEL OF CONFIDENCE CAN ONE STREAM OF INFORMATION BE SUBSTITUTED FOR ANOTHER ONE: SMALL-SCALE TESTING FOR FULL-SCALE TESTING MODEL-BASED PREDICTIONS FOR TESTING FUSION OF HISTORICAL DATA, MODELING AND TESTING

8. Components of a predictive model 1. P 1. Packaging of information Packaging of data: Probabilistic models Fuzzy, convex, etc… models Packaging of knowledge: Mechanistic models Expertise 2. E 2. Experimental data 3. Qoi 3. Quantity of interest Life expectancy Probability of mission success Maximum stress at weld for mission profile Probability of failure etc

9. Difference between predicted and actual performance Error depends both on models of physical behavior as well as the tools and methods to acquire the necessary data for these models.

10. Error budget

11. Interaction of model and data: Unified mathematical framework:

12. Management of uncertainty COORDINATES IN THIS SPACE REPRESENT PROBABILISTIC CONTENT. SENSITIVITY OF PROBABILISTIC STATEMENTS OF BEHAVIOR ON DATA.

13. Multi-scale probabilistic model Index the stochastic process by SCALE. Only measured scales make it into the stochastic model of the parameter: Approximation space is the completion of the hull generated by the measurements. Variability in each measured scale represents the magnitude of the contribution from that scale. We need a set of spatial functions to serve as carriers of fluctuation: WAVELETS are well-adapted to scale-localization.

14. Complex interacting systems: Multi-physics – Multi-scales System complexity is a significant source of uncertainty eg. unmodeled dynamics interaction between fluctuations New tools of probabilistic modeling are being developed for proper representation of complexity: uncertainty joints nonparametric models multi-scale models

15. Applications completed/current in: Structural Dynamics Dynamic Soil-Structure Interaction Structural Acoustics Acoustic Scattering Compressible and Incompressible Flows Micro-Fluidics Reactive Flows: Combustion Reactive Flows: Protein Labeling Fracture/Fatigue of Composites Flow and Transport in Porous Media Rock Mechanics Hydrology and Watershed Management UNDEX Aerodynamics/Aeroelasticity Drilling Collaborations: JHU Sandia WPAFB Universite Marne-la-Vallee Universite d’Evry University of Oklahoma Taisei Corporation

16. On the Horizon 1. Cmodels 1. Critical examination of probabilistic models of data: 1. Physical and mathematical implications of these models. 2. Connection to multi-scale properties of materials and systems. 3. Adapted bases for enhanced convergence. 2. Enumerical 2. Efficient numerical solvers: 1. Using existing codes. 2. Very high-dimensional quadrature. 3. Intrusive algorithms. 3. Visualization 3. Visualization of probabilistic information as decision aids. 4. Model reductions 4. Model reductions that maximize information content. 5. Optimization 5. Optimization under uncertainty: uncertainty in objective function, decision variables, and constraints. 6. Validation 6. Validation of complex interacting systems. 7. Error estimation 7. Error estimation and refinement: allocation of resources to physical and numerical experiments. 8. Fusion 8. Fusion of experiments and model-based predictions.